Existing emotional support conversation systems mainly focus on one-on-one seeker-supporter interactions and individual emotional states, leaving interpersonal relations in multi-party scenarios underexplored. In this work, we introduce relation-aware emotional support conversation, a new task that evaluates whether LLMs can capture and utilize the evolving dynamics of relationships to offer more effective emotional support. We construct RESCUE (Relation-aware Emotional Support Conversation Understanding and Evaluation Benchmark) from real couple and family interview conversations, containing 191 samples, 7,079 annotated turns, and 1,064.8 minutes of video. Based on rich annotations of socio-emotional and support-related dynamics, RESCUE defines six tasks that evaluate two core capabilities required for relation-aware emotional support: Relational Understanding and Relation-Sensitive Support. Experiments with ten LLMs show that current models perform relatively well on tasks relying on local emotional or intervention cues, but struggle with relation-intensive tasks such as relation pattern prediction, viewpoint prediction, and support strategy prediction. These findings reveal the limitations of current LLMs in modeling interpersonal relations and making relation-sensitive support decisions.

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